Group #14561531 — subgroups

Subgroups — #14561531

Order 2432.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×#64520	—	2	1	no	—
6	C₂²×C₁₉⋊C₈	—	2	1	no	—
7	C₁₉×C₄⋊C₈	—	2	1	no	—
8	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
9	C₄×C₈×C₁₉	—	2	1	no	—
10	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
13	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₁₉	—	2	2	no	—
18	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₄²×C₁₉	D₄	1	1	yes	characteristic
22	#64520	—	4	1	no	—
23	#64520	—	4	1	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂×C₁₉⋊C₈	—	2	2	no	—
26	C₂×C₁₉⋊C₈	—	4	1	no	—
27	C₂×C₁₉⋊C₈	—	4	1	no	—
28	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
39	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
41	C₈×C₁₉	—	4	2	no	—
42	C₁₉⋊C₈	—	4	2	no	—
43	C₁₉⋊C₈	—	4	2	no	—
44	#1301	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	1	no	—
46	C₂²×C₁₉	—	2	1	no	—
47	C₂²×C₁₉	#95	1	1	yes	characteristic
48	C₂²×C₁₉	#106	1	1	yes	characteristic
49	C₂²×C₁₉	#107	1	1	yes	characteristic
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	#102	1	1	yes	characteristic
54	C₄×C₁₉	#102	1	1	yes	characteristic
55	C₄×C₁₉	#103	1	1	yes	characteristic
56	C₄×C₁₉	#103	1	1	yes	characteristic
57	C₄×C₁₉	#108	1	2	yes	—
58	#431	D₁₉	1	1	yes	characteristic
59	#423	—	19	1	no	—
60	C₂×C₄⋊C₈	—	19	1	no	—
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	—	2	1	no	—
63	C₂×C₁₉	#340	1	1	yes	characteristic
64	C₂×C₁₉	#341	1	1	yes	characteristic
65	C₂×C₁₉	#344	1	1	yes	characteristic
66	C₂×M₁₆	—	38	1	no	—
67	C₂²×C₈	—	38	1	no	—
68	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
69	C₄⋊C₈	—	2	1	no	—
70	C₄⋊C₈	—	19	2	no	—
71	C₄⋊C₈	—	19	2	no	—
72	C₄⋊C₈	—	38	1	no	—
73	C₄⋊C₈	—	38	1	no	—
74	C₂²⋊C₈	Dic₁₉	1	2	yes	—
75	C₄×C₈	—	2	1	no	—
76	C₁₉	#1301	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
78	C₂²×C₄	D₇₆	1	1	yes	characteristic
79	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
80	M₁₆	—	76	1	no	—
81	M₁₆	—	76	1	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	38	2	no	—
84	C₂×C₈	—	38	2	no	—
85	C₂×C₈	—	76	1	no	—
86	C₂×C₈	—	76	1	no	—
87	C₄²	C₄×D₁₉	1	1	yes	characteristic
88	C₄²	C₄×D₁₉	1	1	yes	characteristic
89	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	#64516	1	1	yes	characteristic
95	C₂×C₄	#64516	1	1	yes	characteristic
96	C₂×C₄	D₁₅₂	1	1	yes	characteristic
97	C₂×C₄	Dic₇₆	1	1	yes	characteristic
98	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
99	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
100	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
101	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
102	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
103	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
104	C₈	—	4	2	no	—
105	C₈	—	76	2	no	—
106	C₈	—	76	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	#10597274	1	1	yes	characteristic
110	C₂²	#10597275	1	1	yes	characteristic
111	C₂²	C₁₉⋊#95	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	#10597273	1	1	yes	characteristic
116	C₄	#10597273	1	1	yes	characteristic
117	C₄	#10597278	1	1	yes	characteristic
118	C₄	#10597278	1	1	yes	characteristic
119	C₄	#10597279	1	2	yes	—
120	C₂	—	2	1	no	—
121	C₂	—	2	1	no	—
122	C₂	#11926307	1	1	yes	characteristic
123	C₂	#11926308	1	1	yes	characteristic
124	C₂	#11926314	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

Q₁₆

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1301

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#431

D₁₉

yes

characteristic

#423

—

C₂×C₄⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

Dic₁₉

yes

—

C₄×C₈

—

C₁₉

#1301

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₂³

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

D₁₅₂

yes

characteristic

C₂×C₄

Dic₇₆

yes

characteristic

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

100

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

101

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

102

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

103

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₂²

—

108

C₂²

—

109

C₂²

#10597274

yes

characteristic

110

C₂²

#10597275

yes

characteristic

111

C₂²

C₁₉⋊#95

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#10597273

yes

characteristic

116

C₄

#10597273

yes

characteristic

117

C₄

#10597278

yes

characteristic

118

C₄

#10597278

yes

characteristic

119

C₄

#10597279

yes

—

120

C₂

—

121

C₂

—

122

C₂

#11926307

yes

characteristic

123

C₂

#11926308

yes

characteristic

124

C₂

#11926314

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1301
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄²

Frattini

C₂×C₄²

C₂×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂³×C₁₉

C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
76. C₁₉	#1301	semidirect

H ≅ G/N

type

76. C₁₉

#1301

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11926568	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₁₉×#431	2
#1301	19

subgroup

index

#11926568

C₂×C₄⋊(C₁₉⋊C₈)

C₁₉×#431

#1301

Subgroups — #14561531

Conjugacy classes of subgroups

Complements

Maximal subgroups